A] [1 { 1 (1 n)^ 1}]^ 1 = [1 {1 (1/1 n )}]^ 1 = [1 {1 n 1/1 n}]^ 1 = [1 { n/1 n}]^ 1 = {1 n+n/1 n}^ 1 = [1/1 n]^ 1 = 1 n #160; ...

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Power of a Power

Solve : [1-...

Question

Solve : $[1 - {1 - (1 - n)^{- 1}}]^{- 1}$

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Solution

A] $[1 - {1 - (1 - n)^{- 1}}]^{- 1}$
$= [1 - {1 - (\frac{1}{1 - n})}]^{- 1}$
$= [1 - {\frac{1 - n - 1}{1 - n}}]^{- 1}$
$= [1 - {\frac{- n}{1 - n}}]^{- 1}$
$= {\frac{1 - n + n}{1 - n}}^{- 1} = [\frac{1}{1 - n}]^{- 1} = 1 - n$

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